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There were a total of 10 students taking a graduate level Statistics course. One of the assignments in this course was an exam that was worth a total of 100 points. The professor was keeping a running average of the exam scores as she graded them. After the first 8 exams, the average exam score was an 80. Then after grading the final 2 exams, the average was an 82.    For this problem, answer the following question and explain how you arrived at your answer.  What was the average score of the 9th and 10th exams?

New York City consists of 5 major areas (boroughs), some of which are separated by rivers and are connected via ferries and/or bridges. The 5 boroughs are Manhattan, Brooklyn, Queens, the Bronx, & Staten Island. According to the 2020 Census data for New York City, 16.73% of the population lived in the Bronx, 31.08% lived in Brooklyn, 19.24% lived in Manhattan, 27.32% lived in Queens and 5.63% lived in Staten Island (percentages all rounded to 2 decimal places).  Suppose a researcher wanted to carry out a study of the residents of New York City to gauge their opinions on a wide array of political topics. Furthermore, they wanted to carry out a stratified random sample based on which borough the individuals in their study lived in. If the researcher wanted to randomly survey 50,000 residents, how many individuals from each borough should they select? Make sure to be specific about how many individuals are being selected from each borough, and show your work (i.e. how did you arrive at the answer). 

One way that scientists will track the changes in temperature over time is to compare the average maximum or average minimum daily temperatures in degrees Fahrenheit or Celsius. According to U.S. Climate Data, the average daily maximum temperature (in degrees Fahrenheit) in Denver, Colorado was 64.3 in the 1950s, 64.8 in the 1990s and 65.5 in the 2010s.    Which measurement scale would be the most appropriate for the average daily maximum temperature (measured in degrees Fahrenheit) in Denver, Colorado over this time span?

The Chicago Bulls, led by Michael Jordan, had one of the greatest NBA dynasties of all time. They won a total of 6 NBA championships between 1991 and 1998. During the 1992-1993 season, the Chicago Bulls beat the Phoenix Suns in 6 games to become NBA champions. Michael Jordan scored 246 points total during those 6 games and the number of points he scored each game can be found below.    Michael Jordan Points in 1993 NBA Finals Michael Jordan Points Number of Points (Frequency) Game 1 33 Game 2 41 Game 3 55 Game 4 44 Game 5 42 Game 6 31   Of all the points Michael Jordan scored in the 1993 NBA finals, what percentage of them did he score in game 5? (Make sure to round your answer to 2 decimal places, so if you thought the answer was 65.4321% you would type in 65.43% as your answer). 

A study was conducted in 2023 to try and determine the average commute time for Americans. This data was based on commute times from across the nation. A researcher wanted to see if this data accurately reflected the commute times for drivers in her county so she decided to randomly sample 4000 workers from her county and record their commute times. The data is presented in the table below. Use this information to answer this question.    Commute Times Commute Times Frequency Relative Frequency Cumulative Frequency Cumulative Relative Frequency No Commute 820 20.5% 820 20.5% Less than 15 Minutes A 32% C 52.5% 15 – 29 Minutes 720 18% 2820 D 30 – 59 Minutes 1060 B 3880 97% 60 – 119 Minutes 60 1.5% 3940 98.5% 120 Minutes or More 60 1.5% 4000 100%   Based on the table above, identify the four missing values of A, B, C, and D. Make sure clearly label which number corresponds to each letter and make sure to show your work as to how you arrived at your answer. Simply writing the answers will not earn full-credit on this problem. 

The size (inches in diameter) of a medium size pizza at a large pizza chain was between 12 and 14 inches. The CEO wanted to ensure that their medium pizzas were consistently being made in the correct size, and she specifically wanted to ensure that none of the medium size pizzas were ever less than 12 inches. She decided to order a medium pizza from 12 randomly selected locations and recorded the size of the pizzas (inches in diameter) which can be found in the table below.    Medium Pizza Sizes Pizza Number Diameter (in.) 1 13.227 2 13.736 3 13.175 4 12.656 5 12.524 6 12.049 7 13.516 8 12.945 9 13.612 10 13.99 11 12.529 12 13.776   Using this information, find the standard deviation for the diameter (in inches) for this random sample of medium pizzas. Make sure to round your answer to 3 decimal places. (If you thought the answer was 7.654321 then you would write 7.654 as your answer)

The size (inches in diameter) of a medium size pizza at a large pizza chain was between 12 and 14 inches. The CEO wanted to ensure that their medium pizzas were consistently being made in the correct size, and she specifically wanted to ensure that none of the medium size pizzas were ever less than 12 inches. She decided to order a medium pizza from 12 randomly selected locations and recorded the size of the pizzas (inches in diameter) which can be found in the table below.    Medium Pizza Sizes Pizza Number Diameter (in.) 1 13.227 2 13.736 3 13.175 4 12.656 5 12.524 6 12.049 7 13.516 8 12.945 9 13.612 10 13.99 11 12.529 12 13.776   Using this information, find the variance for the diameter (in inches) for this random sample of medium pizzas. Make sure to round your answer to 3 decimal places. (If you thought the answer was 7.654321 then you would write 7.654 as your answer)

New York City consists of 5 major areas (boroughs), some of which are separated by rivers and are connected via ferries and/or bridges. The 5 boroughs are Manhattan, Brooklyn, Queens, the Bronx, & Staten Island. According to the 2020 Census data for New York City, 16.73% of the population lived in the Bronx, 31.08% lived in Brooklyn, 19.24% lived in Manhattan, 27.32% lived in Queens and 5.63% lived in Staten Island (percentages all rounded to 2 decimal places).  Suppose a researcher wanted to carry out a study of the residents of New York City to gauge their opinions on a wide array of political topics. Furthermore, they wanted to carry out a stratified random sample based on which borough the individuals in their study lived in. If the researcher wanted to randomly survey 30,000 residents, how many individuals from each borough should they select? Make sure to be specific about how many individuals are being selected from each borough, and show your work (i.e. how did you arrive at the answer). 

When it comes to house prices in a certain area, many real estate websites will reference the median home price instead of the average. This is because a small group of very expensive or inexpensive homes can drastically affect the average price, but would not have the same impact on the median.  In Boise, ID the cost of homes had increased about 3.1% from the beginning of 2024 to the beginning of 2025. Below are the listing prices for 12 randomly selected homes for sale in January of 2025 from Boise, ID.    Tacoma House Prices Home Number Cost of House 1 280,000 2 449,000 3 2,250,000 4 759,000 5 299,900 6 439,900 7 1,325,000 8 640,000 9 489,900 10 549,000 11 559,900 12 725,000   Calculate the median home price for this random sample of 12 homes. 

The Chicago Bulls, led by Michael Jordan, had one of the greatest NBA dynasties of all time. They won a total of 6 NBA championships between 1991 and 1998. During the 1992-1993 season, the Chicago Bulls beat the Phoenix Suns in 6 games to become NBA champions. Michael Jordan scored 246 points total during those 6 games and the number of points he scored each game can be found below.    Michael Jordan Points in 1993 NBA Finals Michael Jordan Points Number of Points (Frequency) Game 1 33 Game 2 41 Game 3 55 Game 4 44 Game 5 42 Game 6 31   Of all the points Michael Jordan scored in the 1993 NBA finals, what percentage of them did he score in game 1? (Make sure to round your answer to 2 decimal places, so if you thought the answer was 65.4321% you would type in 65.43% as your answer).